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- Derivada de una función implícitamente dada
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- Derivada de:
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Derivada de (60-x)*e^(x+60)
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Derivada de 5*x/(x+1)
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Derivada de 5x^8-8x+1
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Derivada de (4+x^4)*atan(x^1+4/x)/x^3
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Expresiones idénticas
- (cuatro +x^ cuatro)*atan(x^ uno + cuatro /x)/x^ tres
- (4 más x en el grado 4) multiplicar por arco tangente de gente de (x en el grado 1 más 4 dividir por x) dividir por x al cubo
- (cuatro más x en el grado cuatro) multiplicar por arco tangente de gente de (x en el grado uno más cuatro dividir por x) dividir por x en el grado tres
- (4+x4)*atan(x1+4/x)/x3
- 4+x4*atanx1+4/x/x3
- (4+x⁴)*atan(x^1+4/x)/x³
- (4+x en el grado 4)*atan(x en el grado 1+4/x)/x en el grado 3
- (4+x^4)atan(x^1+4/x)/x^3
- (4+x4)atan(x1+4/x)/x3
- 4+x4atanx1+4/x/x3
- 4+x^4atanx^1+4/x/x^3
- (4+x^4)*atan(x^1+4 dividir por x) dividir por x^3
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Expresiones semejantes
- (4+x^4)*atan(x^1-4/x)/x^3
- (4-x^4)*atan(x^1+4/x)/x^3
- (4+x^4)*arctan(x^1+4/x)/x^3
Derivada de (4+x^4)*atan(x^1+4/x)/x^3
Solución
Ha introducido
[src]
/ 4\ / 1 4\
\4 + x /*atan|x + -|
\ x/
---------------------
3
x
$$\frac{\left(x^{4} + 4\right) \operatorname{atan}{\left(x^{1} + \frac{4}{x} \right)}}{x^{3}}$$
((4 + x^4)*atan(x^1 + 4/x))/x^3
Primera derivada
[src]
/ 4 \ / 4\
|1 - --|*\4 + x /
| 2|
3 / 1 4\ \ x /
4*x *atan|x + -| + -----------------
\ x/ 2
/ 1 4\ / 4\ / 1 4\
1 + |x + -| 3*\4 + x /*atan|x + -|
\ x/ \ x/
------------------------------------- - -----------------------
3 4
x x
$$\frac{4 x^{3} \operatorname{atan}{\left(x^{1} + \frac{4}{x} \right)} + \frac{\left(1 - \frac{4}{x^{2}}\right) \left(x^{4} + 4\right)}{\left(x^{1} + \frac{4}{x}\right)^{2} + 1}}{x^{3}} - \frac{3 \left(x^{4} + 4\right) \operatorname{atan}{\left(x^{1} + \frac{4}{x} \right)}}{x^{4}}$$
Segunda derivada
[src]
/ / 2 \ \
| / / 4 \ / 4\\ | / 4 \ / 4\| |
| | |1 - --|*\4 + x /| | |1 - --| *|x + -|| |
| | | 2| | | | 2| \ x/| |
| | 3 / 4\ \ x / | / 4\ | 4 \ x / | |
| 3*|4*x *atan|x + -| + -----------------| \4 + x /*|- -- + -----------------| |
| | \ x/ 2 | | 3 2 | 3 / 4 \ |
| | / 4\ | | x / 4\ | 4*x *|1 - --| / 4\ / 4\|
| | 1 + |x + -| | | 1 + |x + -| | | 2| 6*\4 + x /*atan|x + -||
| \ \ x/ / 2 / 4\ \ \ x/ / \ x / \ x/|
2*|- ---------------------------------------- + 6*x *atan|x + -| - ----------------------------------- + ------------- + ----------------------|
| x \ x/ 2 2 2 |
| / 4\ / 4\ x |
| 1 + |x + -| 1 + |x + -| |
\ \ x/ \ x/ /
------------------------------------------------------------------------------------------------------------------------------------------------
3
x
$$\frac{2 \left(\frac{4 x^{3} \left(1 - \frac{4}{x^{2}}\right)}{\left(x + \frac{4}{x}\right)^{2} + 1} + 6 x^{2} \operatorname{atan}{\left(x + \frac{4}{x} \right)} - \frac{\left(x^{4} + 4\right) \left(\frac{\left(1 - \frac{4}{x^{2}}\right)^{2} \left(x + \frac{4}{x}\right)}{\left(x + \frac{4}{x}\right)^{2} + 1} - \frac{4}{x^{3}}\right)}{\left(x + \frac{4}{x}\right)^{2} + 1} - \frac{3 \left(4 x^{3} \operatorname{atan}{\left(x + \frac{4}{x} \right)} + \frac{\left(1 - \frac{4}{x^{2}}\right) \left(x^{4} + 4\right)}{\left(x + \frac{4}{x}\right)^{2} + 1}\right)}{x} + \frac{6 \left(x^{4} + 4\right) \operatorname{atan}{\left(x + \frac{4}{x} \right)}}{x^{2}}\right)}{x^{3}}$$
Tercera derivada
[src]
/ / / 2 \ \ \
| | | / 4 \ / 4\| | |
| | | |1 - --| *|x + -|| | |
| | | | 2| \ x/| | |
| | / 4\ | 4 \ x / | | / 3 3 2 \ |
| | \4 + x /*|- -- + -----------------| | | / 4 \ / 4 \ / 4\ / 4 \ / 4\| / 2 \ |
| | | 3 2 | 3 / 4 \| / / 4 \ / 4\\ | |1 - --| 4*|1 - --| *|x + -| 24*|1 - --|*|x + -|| | / 4 \ / 4\| |
| | | x / 4\ | 4*x *|1 - --|| | |1 - --|*\4 + x /| | | 2| | 2| \ x/ | 2| \ x/| | |1 - --| *|x + -|| |
| | | 1 + |x + -| | | 2|| | | 2| | / 4\ |12 \ x / \ x / \ x / | | | 2| \ x/| |
| | 2 / 4\ \ \ x/ / \ x /| | 3 / 4\ \ x / | \4 + x /*|-- + ------------ - -------------------- + -------------------| 3 | 4 \ x / | |
| 9*|6*x *atan|x + -| - ----------------------------------- + -------------| 18*|4*x *atan|x + -| + -----------------| | 4 2 2 / 2\ | 12*x *|- -- + -----------------| |
| | \ x/ 2 2| | \ x/ 2 | |x / 4\ / 2\ 3 | / 4\ | | | 3 2 | 2 / 4 \|
| | / 4\ / 4\ | | / 4\ | | 1 + |x + -| | / 4\ | x *|1 + |x + -| | | / 4\ / 4\ | x / 4\ | 18*x *|1 - --||
| | 1 + |x + -| 1 + |x + -| | | 1 + |x + -| | | \ x/ |1 + |x + -| | \ \ x/ / | 30*\4 + x /*atan|x + -| | 1 + |x + -| | | 2||
| \ \ x/ \ x/ / / 4\ \ \ x/ / \ \ \ x/ / / \ x/ \ \ x/ / \ x /|
2*|- -------------------------------------------------------------------------- + 12*x*atan|x + -| + ----------------------------------------- - ------------------------------------------------------------------------- - ----------------------- - -------------------------------- + --------------|
| x \ x/ 2 2 3 2 2 |
| x / 4\ x / 4\ / 4\ |
| 1 + |x + -| 1 + |x + -| 1 + |x + -| |
\ \ x/ \ x/ \ x/ /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3
x
$$\frac{2 \left(- \frac{12 x^{3} \left(\frac{\left(1 - \frac{4}{x^{2}}\right)^{2} \left(x + \frac{4}{x}\right)}{\left(x + \frac{4}{x}\right)^{2} + 1} - \frac{4}{x^{3}}\right)}{\left(x + \frac{4}{x}\right)^{2} + 1} + \frac{18 x^{2} \left(1 - \frac{4}{x^{2}}\right)}{\left(x + \frac{4}{x}\right)^{2} + 1} + 12 x \operatorname{atan}{\left(x + \frac{4}{x} \right)} - \frac{\left(x^{4} + 4\right) \left(- \frac{4 \left(1 - \frac{4}{x^{2}}\right)^{3} \left(x + \frac{4}{x}\right)^{2}}{\left(\left(x + \frac{4}{x}\right)^{2} + 1\right)^{2}} + \frac{\left(1 - \frac{4}{x^{2}}\right)^{3}}{\left(x + \frac{4}{x}\right)^{2} + 1} + \frac{24 \left(1 - \frac{4}{x^{2}}\right) \left(x + \frac{4}{x}\right)}{x^{3} \left(\left(x + \frac{4}{x}\right)^{2} + 1\right)} + \frac{12}{x^{4}}\right)}{\left(x + \frac{4}{x}\right)^{2} + 1} - \frac{9 \left(\frac{4 x^{3} \left(1 - \frac{4}{x^{2}}\right)}{\left(x + \frac{4}{x}\right)^{2} + 1} + 6 x^{2} \operatorname{atan}{\left(x + \frac{4}{x} \right)} - \frac{\left(x^{4} + 4\right) \left(\frac{\left(1 - \frac{4}{x^{2}}\right)^{2} \left(x + \frac{4}{x}\right)}{\left(x + \frac{4}{x}\right)^{2} + 1} - \frac{4}{x^{3}}\right)}{\left(x + \frac{4}{x}\right)^{2} + 1}\right)}{x} + \frac{18 \left(4 x^{3} \operatorname{atan}{\left(x + \frac{4}{x} \right)} + \frac{\left(1 - \frac{4}{x^{2}}\right) \left(x^{4} + 4\right)}{\left(x + \frac{4}{x}\right)^{2} + 1}\right)}{x^{2}} - \frac{30 \left(x^{4} + 4\right) \operatorname{atan}{\left(x + \frac{4}{x} \right)}}{x^{3}}\right)}{x^{3}}$$
Gráfico